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Power divider achieves matched impedance at all ports at the cost of 6 dB powerloss. If you don't know why to use it, you probably don't need it and may use a T-connector as well.
The t-junction is a power divider (3 ports network) that has the following properties:
It's a lossless network.
It's reciprocal.
BUT, it can't be matched at all ports
There are another kind of power divider that uses resistors (resistive dividers, wilkinson power dividers) that:
Are reciprocal
All ports can be matched
BUT, are not lossless networks.
The above-mentioned is because the impossibility to synthesize/create 3 ports networks with the 3 properties simultaneously.
My first comment is that there are a number of errors above. Use the information but check carefully that you understand the part you intend to apply.
Power dividers are used to either separate or combine signals. Numerous factors need to be considered including size, cost, bandwidth, frequency of operation, match and s11, insertion loss, isolation, phase (particularly in hybrids), performance changes as the strength and phase of input signal(s) change, dispersion, power handling, etc.
The issue is deceptively simple and can get quite convoluted. Find a text on the subject and do some reading.
Three cables can simply be connected but there are potential issues of s11, s21 and isolation. It is certainly inexpensive. Usually when something is cheap it also works badly and this is the case here. Of course, we need to understand "works badly".
The term power divider may be ambiguous. I understand it designating a resistive power divider. A 50 ohms resistive power divider e. g. is a T-circuit with three 16.7 ohms resistors, achieving the said 6 dB attenuation. It is generally used in labs for splitting and combining signals when impedance matching is required. The components are wideband 0 - x Ghz.
The "lossless" components are usually designated power splitters, they have limited bandwith, and are bulky and expensive. They are used in specific applications, where loss matters.
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