Allah has no Partner or Associate
Allah declares Himself to be above having any child or partner in dominion, control and worship. He says:
مَا اتَّخَذَ اللَّهُ مِن وَلَدٍ وَمَا كَانَ مَعَهُ مِنْ إِلَـهٍ إِذاً لَّذَهَبَ كُلُّ إِلَـهٍ بِمَا خَلَقَ وَلَعَلاَ بَعْضُهُمْ عَلَى بَعْضٍ
(No son did Allah beget, nor is there any god along with Him. (If there had been many gods), then each god would have taken away what he had created, and some would have tried to overcome others.) meaning, if it were decreed that there should be a plurality of deities, each of them would have exclusive control over whatever he had created, so there would never be any order in the universe. But what we see is that the universe is ordered and cohesive, with the upper and lower realms connected to one another in the most perfect fashion.
مَّا تَرَى فِى خَلْقِ الرَّحْمَـنِ مِن تَفَـوُتٍ
(you can see no fault in the creation of the Most Gracious) 65:3. Moreover, if there were a number of gods, each of them would try to subdue the other with enmity, and one would prevail over the other. This has been mentioned by the scholars of `Ilm-ul-Kalam, who discussed it using the evidence of mutual resistance or counteraction. This idea states that if there were two or more creators, one would want to make a body move while the other would want to keep it immobile, and if neither of them could achieve what they wanted, then both would be incapable, but the One Whose existence is essential i.e., Allah cannot be incapable. It is impossible for the will of both to be fulfilled because of the conflict. This dilemma only arises when a plurality of gods is suggested, so it is impossible for there to be such a plurality, because if the will of one is fulfilled and not the other, the one who prevails will be the one whose existence is essential (i.e., God) and the one who is prevailed over will be merely possible (i.e., he is not divine), because it is not befitting for the one to be defeated whose existence is essential. Allah says:
وَلَعَلاَ بَعْضُهُمْ عَلَى بَعْضٍ سُبْحَـنَ اللَّهِ عَمَّا يَصِفُونَ
(and some would have tried to overcome others! Glorified be Allah above all that they attribute to Him!) meaning, high above all that the stubborn wrongdoers say when they claim that He has a son or partner.
عَـلِمُ الْغَيْبِ وَالشَّهَـدَةِ
(All-Knower of the unseen and the seen!) means, He knows what is hidden from His creatures and what they see.
فَتَعَـلَى عَمَّا يُشْرِكُونَ
(Exalted be He over all that they associate as partners to Him!) means, sanctified and glorified and exalted be He above all that the wrongdoers and liars say.