Self-similar fractals provide a degree of freedom for varying the resonance frequency due to the multiscale geometric features involved and are an ideal candidate for ultrabroadband absorbing devices - especially in the terahertz (THz) band where there is a lack of natural absorbing materials. Metasurface-based THz absorbers often suffer from poor broadband performance, whereas strongly absorbing broadband devices are typically complex multilayer structures. Here, we numerically demonstrate an ultrabroadband, ultrathin, polarization-insensitive, wide-angle, single-layer planar metasurface THz absorber by integrating different Cayley tree fractal resonators into one supercell based on the frequency shifting and multiresonance bands of different fractal orders. In terms of physics, we have exploited the self-similar nature of fractal geometry to engineer the multimodal spectrum of this system. With increasing fractal order N, an increasing number of modes can be excited with certain degeneracies where each mode corresponds to plasmon oscillations at different geometric scales inside fractal. As a result, broad, multipeaked spectra with large degeneracy numbers can be achieved with larger N. Finally, by placing fractals of different order N into one supercell, the coupling and superposition of the neighboring resonances exhibit the desired ultrabroadband response. The proposed absorber provides a wide incident wave angle with a full-width half-maximum absorption bandwidth of more than one octave, i.e. 3.88 THz. Greater than 80% absorption is achieved over a frequency range of 3 THz. Owing to its performance, this work is a step forward in realizing perfect blackbody absorbers that can be easily integrated with bolometric sensing technology to make high-efficient THz-sensing devices.