In this case, since you just need to bring one column, .map is probably more suitable. We take the first value within each EMM_ID group and only map that value. Alignment on index ensures the rest become NaN.
Sample Data
import pandas as pd
import numpy as np
df_x = pd.DataFrame({'EMM_ID': [610462, 610462, 610462, 610462, 61000, 61000],
'ID_home': [np.NaN, np.NaN, np.NaN, np.NaN, np.NaN, np.NaN]})
df_y = pd.DataFrame({'EMM_ID': [610462, 61000], 'ID_home': [81000, 18]})
Code
df_x['ID_home'] = df_x.groupby('EMM_ID').head(1).EMM_ID.map(df_y.set_index('EMM_ID').ID_home)
Output: df_x
EMM_ID ID_home
0 610462 81000.0
1 610462 NaN
2 610462 NaN
3 610462 NaN
4 61000 18.0
5 61000 NaN
If you need to bring multiple columns, then you could split your DataFrame, merge with the subset, and then concatenate back to one DataFrame.
df_x = pd.DataFrame({'EMM_ID': [610462,610462,610462,610462, 61000, 61000],
'ID_home': [np.NaN, np.NaN, np.NaN, np.NaN, np.NaN, np.NaN]})
df_y = pd.DataFrame({'EMM_ID': [610462, 61000], 'ID_home': [81000, 18], 'Val_2': ['A', 'F']})
to_merge = df_x.groupby('EMM_ID').head(1)
keep = df_x[~df_x.index.isin(to_merge.index)]
pd.concat([keep, to_merge[['EMM_ID']].merge(df_y)], sort=False).sort_index()
Output:
EMM_ID ID_home Val_2
0 610462 81000.0 A
1 610462 NaN NaN
1 61000 18.0 F
2 610462 NaN NaN
3 610462 NaN NaN
5 61000 NaN NaN