Is it permissible for a father to divide a plot of land equally between his two sons to be registered in their names, and to sell another plot of land and divide its price between them for construction, while the house remains in the father’s name, given the father’s fear of the impermissibility of registering the land on which the son will build his own money?

There is no blame upon a father for gifting whatever he wishes of money or lands to his children, as long as he is not in a life-threatening illness. However, he is obliged to be just between all his children, male and female, without preferring some over others, unless there is a legitimate شرعي justification. If he has only two children, he may give them whatever he wishes, provided there is justice between them.