Limitations in A* algorithm

I have 2 questions:

1. How its called an algorithm that works as A*, but instead of inserting all the neighbors of the selected node in the priority queue, it insert only the best k.
2. How its called an algorithm that works as A*, so it insert all the neighbors of the selected node in the priority queue, but this priority queue has a limited size h, so if in it there are more than h element, the algoritmh drop the worst node. I think it is a simple version of SMA*.

I know that these algorithms are not optmal, but they look like to work very well in my project. And I want to know if they have been studied in past. I don't find anything userfull in the internet.