Using multiple DbContexts with a generic repository and unit of work

My application is getting larger and so far I have a single MyDbContext which has all the tables I need in my application. I wish (for the sake of overview) to split them up into multiple DbContext, like MainDbContext, EstateModuleDbContext, AnotherModuleDbContext and UserDbContext.

I am unsure how this is done probably as I am right now using dependecy injection (ninject) to place my DbContext on my UnitOfWork class like:

kernel.Bind(typeof(IUnitOfWork)).To(typeof(UnitOfWork<MyDbContext>));

Should I drop this approach with dependency injection and explicit set the DbContext I wish to use on my services like:

private readonly EstateService _estateService;

public HomeController()
{
    IUnitOfWork uow = new UnitOfWork<MyDbContext>();
    _estateService = new EstateService(uow);
}

Instead of:

private readonly EstateService _estateService;

public HomeController(IUnitOfWork uow)
{
    _estateService = new EstateService(uow);
}

Or this there another better approach? Also as a side question, I dont like passing the uow to my service - is there another (better) approach?

Code

I have this IDbContext and MyDbContext:

public interface IDbContext
{
    DbSet<T> Set<T>() where T : class;

    DbEntityEntry<T> Entry<T>(T entity) where T : class;

    int SaveChanges();

    void Dispose();
}

public class MyDbContext : DbContext, IDbContext
{
    public DbSet<Table1> Table1 { get; set; }
    public DbSet<Table2> Table1 { get; set; }
    public DbSet<Table3> Table1 { get; set; }
    public DbSet<Table4> Table1 { get; set; }
    public DbSet<Table5> Table1 { get; set; }
    /* and so on */

    static MyDbContext()
    {
        Database.SetInitializer<MyDbContext>(new CreateDatabaseIfNotExists<MyDbContext>());
    }

    public MyDbContext()
        : base("MyDbContext")
    {
    }

    protected override void OnModelCreating(DbModelBuilder modelBuilder)
    {

    }
}

Then I have this IRepository and the implementation:

public interface IRepository<T> where T : class
{
    IQueryable<T> GetAll();

    void Add(T entity);

    void Delete(T entity);

    void DeleteAll(IEnumerable<T> entity);

    void Update(T entity);

    bool Any();
}

public class Repository<T> : IRepository<T> where T : class
{
    private readonly IDbContext _context;
    private readonly IDbSet<T> _dbset;

    public Repository(IDbContext context)
    {
        _context = context;
        _dbset = context.Set<T>();
    }

    public virtual IQueryable<T> GetAll()
    {
        return _dbset;
    }

    public virtual void Add(T entity)
    {
        _dbset.Add(entity);
    }

    public virtual void Delete(T entity)
    {
        var entry = _context.Entry(entity);
        entry.State = EntityState.Deleted;
        _dbset.Remove(entity);
    }

    public virtual void DeleteAll(IEnumerable<T> entity)
    {
        foreach (var ent in entity)
        {
            var entry = _context.Entry(ent);
            entry.State = EntityState.Deleted;
            _dbset.Remove(ent);
        }
    }

    public virtual void Update(T entity)
    {
        var entry = _context.Entry(entity);
        _dbset.Attach(entity);
        entry.State = EntityState.Modified;
    }

    public virtual bool Any()
    {
        return _dbset.Any();
    }
}

And the IUnitOfWork and implemention which handles the work done with the DbContext

public interface IUnitOfWork : IDisposable
{
    IRepository<TEntity> GetRepository<TEntity>() where TEntity : class;

    void Save();
}

public class UnitOfWork<TContext> : IUnitOfWork where TContext : IDbContext, new()
{
    private readonly IDbContext _ctx;
    private readonly Dictionary<Type, object> _repositories;
    private bool _disposed;

    public UnitOfWork()
    {
        _ctx = new TContext();
        _repositories = new Dictionary<Type, object>();
        _disposed = false;
    }

    public IRepository<TEntity> GetRepository<TEntity>() where TEntity : class
    {
        // Checks if the Dictionary Key contains the Model class
        if (_repositories.Keys.Contains(typeof(TEntity)))
        {
            // Return the repository for that Model class
            return _repositories[typeof(TEntity)] as IRepository<TEntity>;
        }

        // If the repository for that Model class doesn't exist, create it
        var repository = new Repository<TEntity>(_ctx);

        // Add it to the dictionary
        _repositories.Add(typeof(TEntity), repository);

        return repository;
    }

    public void Save()
    {
        _ctx.SaveChanges();
    }

    public void Dispose()
    {
        Dispose(true);
        GC.SuppressFinalize(this);
    }

    protected virtual void Dispose(bool disposing)
    {
        if (this._disposed) return;

        if (disposing)
        {
            _ctx.Dispose();
        }

        this._disposed = true;
    }
}